In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the function: T(t)= 70 + 19sin((pi*t)/12). What is the temperature at 3 pm?
at 3pm, t=6, so
T(6)= 70 + 19sin((pi*6)/12) = 70+19 = 89
To find the temperature at 3 pm, we need to determine the value of T(t) when t equals 6.
Given the function T(t) = 70 + 19sin((πt)/12), we substitute t = 6 into the equation:
T(6) = 70 + 19sin((π*6)/12)
= 70 + 19sin(π/2)
= 70 + 19sin(90°)
Now, let's calculate the value of sin(90°), which is equal to 1:
T(6) = 70 + 19 * 1
= 70 + 19
= 89
Therefore, the temperature at 3 pm is 89 degrees Fahrenheit.